TSTP Solution File: SYO900^11 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO900^11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 19:35:15 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_p,type,
p: mworld > $o ).
thf(ty_eigen__2,type,
eigen__2: mworld ).
thf(ty_q,type,
q: mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: mworld ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__3,type,
eigen__3: mworld ).
thf(ty_mactual,type,
mactual: mworld ).
thf(sP1,plain,
( sP1
<=> ( mrel @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( mrel @ eigen__2 @ eigen__0 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: mworld,X2: mworld] :
( ~ ( ( mrel @ eigen__2 @ X2 )
=> ~ ( mrel @ eigen__2 @ X1 ) )
=> ( mrel @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: mworld] :
( ~ ( ( mrel @ eigen__2 @ X1 )
=> ~ sP1 )
=> ( mrel @ X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: mworld,X2: mworld] :
( ~ ( ( mrel @ mactual @ X2 )
=> ~ ( mrel @ mactual @ X1 ) )
=> ( mrel @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( mrel @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: mworld] :
( ~ ( ( mrel @ mactual @ X1 )
=> ~ ( mrel @ mactual @ eigen__0 ) )
=> ( mrel @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP3
=> ( mrel @ eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( mrel @ eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: mworld,X2: mworld,X3: mworld] :
( ~ ( ( mrel @ X1 @ X3 )
=> ~ ( mrel @ X1 @ X2 ) )
=> ( mrel @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ( mrel @ mactual @ eigen__2 )
=> ~ ( mrel @ mactual @ eigen__0 ) )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( p @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( mrel @ mactual @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( mrel @ mactual @ eigen__2 )
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( mrel @ mactual @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP10
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(def_mlocal,definition,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) ).
thf(con,conjecture,
( ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) ) ) )
=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) ) ) )
=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP14
=> ( sP2
=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( q @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP14,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP2
=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( q @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP2,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( q @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ( mrel @ eigen__0 @ eigen__1 )
=> ( q @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
mrel @ eigen__0 @ eigen__1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( q @ eigen__1 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP16
=> ( ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( q @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( p @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP16,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( q @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( p @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( q @ X1 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( p @ X1 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP1
=> sP13 ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP1,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP12
| sP15
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP15
| ~ sP16
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP11
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP5
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| sP3
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP3
| ~ sP7
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP11
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP2
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP17
| ~ sP10
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(mrel_euclidean,axiom,
sP11 ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h16,h14,h15,h12,h13,h11,h9,h10,h8,h6,h7,h4,h5,h3,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,mrel_euclidean,h4,h6,h12,h17,h18]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h12,h13,h11,h9,h10,h8,h6,h7,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h16,13,h17,h18]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h11,h9,h10,h8,h6,h7,h4,h5,h3,h1,h2,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__3)],[h15,14,h16]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h9,h10,h8,h6,h7,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,15,h14,h15]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,16,h12,h13]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h2,17,h11]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,18,h9,h10]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,19,h8]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,20,h6,h7]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,21,h4,h5]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h1,22,h3]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,23,h1,h2]) ).
thf(0,theorem,
( ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) ) ) )
=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[24,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO900^11 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 08:12:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 25
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------